Improvement on Aberth's method for choosing initial approximations to zeros of polynomials

1989 ◽  
Vol 136 (2) ◽  
pp. 101 ◽  
Author(s):  
Yuji Nagashima ◽  
Taki Kanda ◽  
Hideyo Nagashima
Keyword(s):  
Zeros Of Polynomials

scholarly journals On the growth and zeros of polynomials attached to arithmetic functions

2021 ◽  
Author(s):  
Bernhard Heim ◽  
Markus Neuhauser
Keyword(s):  
Lie Algebras ◽  
Chebyshev Polynomials ◽  
Fourier Coefficients ◽  
Arithmetic Functions ◽  
Zeros Of Polynomials ◽  
Simple Complex ◽  
Hook Length ◽  
Moderate Growth ◽  
Growth Properties ◽  
Sum Of Divisors

AbstractIn this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g and h, where g is normalized, of moderate growth, and $$0<h(n) \le h(n+1)$$ 0 < h ( n ) ≤ h ( n + 1 ) . We put $$P_0^{g,h}(x)=1$$ P 0 g , h ( x ) = 1 and $$\begin{aligned} P_n^{g,h}(x) := \frac{x}{h(n)} \sum _{k=1}^{n} g(k) \, P_{n-k}^{g,h}(x). \end{aligned}$$ P n g , h ( x ) : = x h ( n ) ∑ k = 1 n g ( k ) P n - k g , h ( x ) . As an application we obtain the best known result on the domain of the non-vanishing of the Fourier coefficients of powers of the Dedekind $$\eta $$ η -function. Here, g is the sum of divisors and h the identity function. Kostant’s result on the representation of simple complex Lie algebras and Han’s results on the Nekrasov–Okounkov hook length formula are extended. The polynomials are related to reciprocals of Eisenstein series, Klein’s j-invariant, and Chebyshev polynomials of the second kind.

Sum rules for zeros of polynomials. I

1980 ◽  
Vol 21 (4) ◽  
pp. 702-708 ◽  
Author(s):  
K. M. Case
Keyword(s):  
Sum Rules ◽  
Zeros Of Polynomials

A Note on the Geometry of Zeros of Polynomials

1971 ◽  
Vol 44 (3) ◽  
pp. 157 ◽  
Author(s):  
C. A. Long
Keyword(s):  
Zeros Of Polynomials

On the Zeros of Polynomials

1965 ◽  
Vol 72 (6) ◽  
pp. 631 ◽  
Author(s):  
Q. G. Mohammad
Keyword(s):  
Zeros Of Polynomials

scholarly journals General numerical radius inequalities for matrices of operators

2016 ◽  
Vol 14 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Mohammed Al-Dolat ◽  
Khaldoun Al-Zoubi ◽  
Mohammed Ali ◽  
Feras Bani-Ahmad
Keyword(s):  
Lower Bounds ◽  
Upper Bounds ◽  
Zeros Of Polynomials ◽  
Numerical Radius

AbstractLet Ai ∈ B(H), (i = 1, 2, ..., n), and $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.

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